We introduce Auslander-Reiten sequences for group algebras and give several recent applications. The first part of the paper is devoted to some fundamental problems in Tate cohomology which are motivated by homotopy theory. In the second part of the paper we interpret Auslander-Reiten sequences in the context of Galois theory and connect them to some important arithmetic objects.

We use Arakelov theory to define a height on divisors of degree zero on a hyperelliptic curve over a global field, and show that this height has computably bounded difference from the Néron–Tate height of the corresponding point on the Jacobian. We give an algorithm to compute the set of points of bounded height with respect to this new height. This provides an ‘in principle’ solution to the pr...

The goal of local class field theory is to classify abelian Galois extensions of a local field K. Several definitions of local fields are in use. In this thesis, local fields, which will be defined explicitly in Section 2, are fields that are complete with respect to a discrete valuation and have a finite residue field. A prototypical first example is Qp, the completion of Q with respect to the...

We consider brave new cochain extensions F (BG+, R) −→ F (EG+, R), where R is either a Lubin-Tate spectrum En or the related 2-periodic Morava K-theory Kn, and G is a finite group. When R is an Eilenberg-Mac Lane spectrum, in some good cases such an extension is a G-Galois extension in the sense of John Rognes, but not always faithful. We prove that for En and Kn these extensions are always fai...

— We give a short proof of a conjecture of Lubin concerning certain families of p-adic power series that commute under composition. We prove that if the family is full (large enough), there exists a Lubin-Tate formal group such that all the power series in the family are endomorphisms of this group. The proof uses ramification theory and some p-adic Hodge theory.

objectives: in this research we evaluate an individually family-based dohsa exercise programme of balance in the aged people and its effect on self confidence for performing common daily tasks with less falling could be influenced by training. methods: from a residential care center, five aged person were participated in this study. they were trained by dohsa method for six weeks. two types of ...

§0. Introduction §1. The Tate Conjecture as a Sort of Grothendieck Conjecture §1.1. The Tate Conjecture for non-CM Elliptic Curves §1.2. Some Pro-p Group Theory §2. Hyperbolic Curves as their own “Anabelian Albanese Varieties” §2.1. A Corollary of the Main Theorem of [Mzk2] §2.2. A Partial Generalization to Finite Characteristic §3. Discrete Real Anabelian Geometry §3.1. Real Complex Manifolds ...

Since Tate pairing was suggested to construct a cryptosystem, fast computation of Tate pairing has been researched recently. Barreto et. al[3] and Galbraith[8] provided efficient algorithms for Tate pairing on y = x − x + b in characteristic 3 and Duursma and Lee[6] gave a closed formula for Tate pairing on y = x − x + d in characteristic p. In this paper, we present completely general and expl...